How can I count the number of reads supporting a specific splice junction (e.g. chr1:15000-20000 where 15000 is the splice donor and 20000 is the splice acceptore position) in a RNA-Seq bam file aligned with STAR ?

If you don't have that then you'd have to follow Irsan's suggestion. Of course, this would likely mean needing to code something since I don't personally know anything that would do it. In theory, that should be possible with a bit of pysam to get the splice junctions. The simplest method would then be to write a script to output only splice junctions and then to pipe that to sort and then uniq -c followed by awk to reformat. The performance might not be optimal, but for an ad hoc solution I figure that'd work.

In the *.Log.final.out the number of introns/splices are recorded but I am not sure if this this is the number of spliced reads. I have checked the manual but couldn't find an answer. A read can be spliced multiple times of course.

What is the possible way, to count the spliced reads (over introns). I want to count it for all the introns. Is there any method to extract that information from IGV? I can see in sashmi plot, it shows the spliced read count for each intron.